This paper presents an impedance-based contact control of a free-flying space robot with respect to the coefficient of restitution. Since no object is constrained in space, the contact between two objects in orbit must be treated carefully so as to prevent the objects from inducing undesired contact force and post-contact relative motion. As a solution to this issue, the authors propose a contact control method for a free-flying space robot based on the impedance control with respect to the coefficient of restitution. The coefficient of restitution is used as a reference value to tune the impedance parameters and is formulated through dynamic consideration to include both the impedance parameters and contact parameters in the coefficient of restitution. The fundamental experiment is conducted to verify the proposed control method, using a ground-based manipulator to realize the impedance control, and a fixed wall as a target surface. The experimental results showed that the proposed control method successfully controlled the coefficient of restitution between two bodies.